how do i solve this. I set the sins equal to each other with the numbers that were given and got 84.18349, but it's not the right answer

Question

Given a triangle with angle A = 99 degrees and sides a = 37 and b = 14. Find side c.

Answer 1

a/sinα=b/sinβ=c/sinγ

37/sin99°=37.461=14/sinα; α=21.945°;

180-99-21.945=59.05°=β.

b/sinβ=37.461=b/sin59.05=b/.857; 37.461*.857=32.083=b

To label a triangle:

side a is shortest

b mid

c hypotenuse

angle α opposite a

β b

γ c

Answer 2

You first have to find the measure of angle C before you can use the Law of Sines to find side c.

sinB/14 = sin99/37

So B equals inverse sine of 14sin99/37.

Once you have B, then C = 180 - (B + 99).

Now with C you have c/sinC = 37/sin99 => c = 37sinC/sin99.

The answer can be found here, but see if you can get it on your own first.

desmos.com/calculator/gd8pl12pmx